A simple graph is reflexive if the second largest eigenvalue of its (0, 1) adjacency matrix does not exceed 2. A graph is a cactus, or a treelike graph, if any pair of its cycles (circuits) has at most one common vertex. The subject of this paper is the class of tricyclic cactuses in which the central cycle is a quadrangle touching the rest two cycles at its non-adjacent vertices. In this class we describe a set of maximal reflexive graphs. The so-called "pouring" of Smith trees plays the crucial role in characterizing the resulting set.
The aim of this paper is to examine the families of monotonically stratified
functions with respect to one parameter and the connections of such families
of functions with certain results stemming from the Theory of Analytic Inequalities. The obtained results are applied to the Cusa-Huygens inequality
and some related inequalities.
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